Turns out that Charlie is going to be a green and blue owl, so those were the colors I went with. Here is the process-- I made the chin strap and then cast on the rest of the hat in the round.
The main part of the hat was in two colors, one variegated blue and green and one light blue. Then I made a flap at the top in green and the variegated. I didn't want to finish it off in the round, because I needed some "ears" for the owl, so I left the top square and just sewed it together.
Then, after everything was sewed up, I made little tassels for the ends of the ears.
After the main part of the hat was constructed, I wove in the ends and attached a button. I found a little blue button that worked perfectly with the color of the hat.
Then I finished it off with the felt eyes and beak you saw above. It turned out so cute. I'm really happy with it, and I think little Charlie will look adorable in it. I'll see if I can get some pictures of the little guy wearing the hat to get the full affect.